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OneStone® Pebbles Surfaces of Revolution

The Surfaces of Revolution Pebble provides a high-quality visualization for what is often percieved to be one of the more difficult topics in the calculus syllabus. The 2D display shows a user-defined 2D curve, while the 3D display shows the surface created by rotating the 2D curve about an axis. The curve and surface can be animated by varying any constant in the expression, as described on the Using Pebbles page.

This Pebble accepts all the standard math operators plus the variable X or Y; expressions may use one or the other, but not both. Functions are graphed according to the following rules:

  • Functions in which X is the only independent variable are drawn in the 2D Graph as the curve Y = F(X). This curve is then rotated about the X axis to form the surface shown in the 3D graph.
  • Functions in which Y is the only independent variable are drawn in the 2D Graph as X = F(Y). This curve is then rotated about the Y axis to form the surface shown in the 3D graph.

Click the 'Launch...' link below to start the Surfaces of Revolution Pebble. The process of installing and running a Pebble for the first time is explained on the Installing Pebbles page. Running one after the first time is quicker: the JOGL package doesn't have to be downloaded, plus something other than the generic 'Starting Java' image is displayed during start-up.

A special thanks to Dr. Bryan Shader of the University of Wyoming for suggesting this topic.


Before launching the Pebble you must agree to the End User License Agreement. In brief, it says you won't claim the work to be your own, you won't attempt to resell it and you won't attempt to disassemble it.

I agree to the license terms found here.
Click Here to
Launch the Surfaces of Revolution Pebble.

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